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semilinear parabolic equation; functional differential equation; integrodifferential equation; integral equation fractional evolution equation; global existence; stability; variation of parameters
We prove global existence and stability results for a semilinear parabolic equation, a semilinear functional equation and a semilinear integral equation using an inequality which may be viewed as a nonlinear singular version of the well known Gronwall and Bihari inequalities.
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